Problem: Rewrite as a simplified fraction. ${2.54\overline{5} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 2545.5555...\\ 100x &= 254.5555...\end{align*}}$ Subtracting the two equations, we have: ${900x = 2291}$ ${x = \dfrac{2291}{900}} \text{or} {2 \dfrac{491}{900}}$